Principles of Economics (12th Edition)
12th Edition
ISBN: 9780134078779
Author: Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher: PEARSON
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Question
Chapter 14, Problem 3.2P
(a)
To determine
Dominant strategy
(b)
To determine
Strategy
(c)
To determine
Strategy opted.
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Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions.
Player 1
Strategy
C
15, 7
8, 12
a. What is player 1's optimal strategy?
Player 1 does not have an optimal strategy.
Strategy A.
Strategy B.
b. Determine player 1's equilibrium payoff.
Player 2
D
10, 11
19,
7
E
19, 15
12, 3
F
18, 20
15, 16
Question 2:
Consider two players, A and B, each of which can choose action X or Y. Their payoffs are
represented in the following matrix, where K is a constant.
Player A
X
Y
X
A: 15
B: 12
A: 20
B: 30
Player B
Y
A: 18
B: 24
A: 18 + K
B: 22
Q2 a) First assume that K > 0. Does either player have a dominant strategy? If so, explain
what it is and why.
Q2 b) Again assuming that K > 0, explain with appropriate discussion what is the Nash
equilibrium of this game.
Q2 c) Now assume that K<0. Do players have dominant strategies and what is the Nash
equilibrium in this case? Does your answer depend on the specific (negative) value of K?
Explain the reason behind the differences between the results in point c) and those in points
a) and b).
Consider a game in which there is $4 to be divided, and the first mover is only permitted to make one of three proposals:
(a) $3 for the first mover and $1 for the second mover, (b) $2 for each, or (c) $1 for the first movier and $3 for the second
mover. The second mover is shown the proposal and can either accept, in which case it is implemented, or reject and
cause each to earn $0. Show this game in extensive (tree) form. Be sure to show the payoffs for each person, with the
first mover listed on the left, for each of the six terminal nodes.
Chapter 14 Solutions
Principles of Economics (12th Edition)
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